How to look at Risk like a Market Maker

[00:00:03.11] - Speaker 1
Hi, everyone. Good morning, good afternoon. Welcome again to this live. And today, this one is going to be a good one. We have Ryan here. We're going to do some introduction very soon, but this session is on option pricing, option valuation, and how to use GRICs to manage the risk in an option portfolio. We're going to go through, like, an Excel file on how we can calculate the risk, share more information, and then any question. Before I introduce you, Ryan, let's just go through a quick disclaimer very briefly. All right, so I'll pass it on to you, Ryan, maybe, like, for those who don't know you, if you want to maybe give a brief introduction about your role, what you. You're doing, your experience, our partnering together, and then obviously I'll let you take take the lead on this.

[00:01:08.15] - Speaker 2
Yeah, absolutely. Thanks, Fabio. So, again, my name is Ryan Darnell. I'm the founder of Senecal Capital, a hedge fund, a small startup hedge fund in our third year of operation. By background, I was a professional options trader, market maker and, and proprietary trader in options and more complex or structured products and, and derivatives. I did that. I've done that for about 15 years now. And, you know, I work with, with Mentor Q on a variety of things, but, you know, I'm kind of a strategic partner, helping advise on ways to improve option screening and, and market analysis tools, starting my own small startup fund. You know, I'm painfully aware of just how hard it is to get good data and to get the tools that the pros use. And so, you know, I'm not only using these products to help with our analysis, but we're also working constantly with Fabio and his team to put the kind of screens that I would want to use for my fund and that I would have used when I was running a trading desk into your product and make it available to the market because I think everybody should have fair access.

[00:02:21.05] - Speaker 2
So without further ado, I'm going to spend a little time talking today. Unless there's anything else you want me to cover, Fabio, I'm going to spend some. Some time talking about, you know, how to think about options risk. You know, options risk is something that people get really overwhelmed by. There's a lot of, there's a lot of math that, you know, that gets thrown around and people get, you know, people get quite nervous about it. You know, they, they, they hear about Delta and Gamma and Vega and think, like, what all could that be? Oops. I'm going to try to pull up an example of Black Scholes for you all Here, you know, this is technically the option pricing formula. And it's really. If probably everybody can see that. And the fact is, that's really scary, right? Like, most people look at this and go, oh, I don't want to have anything to do with this. But I'm going to show you today that there's the way that practitioners actually do this. You know, you don't have to do any math, you don't have to take any derivatives. You'll be doing that math and you won't even realize it, which is the great part.

[00:03:22.25] - Speaker 2
So, to start with, the first thing to understand is that, you know, my belief is the best way to learn is to just do it yourself. So I'm gonna give everybody a few minutes. Please throw in the comments if you're having any issues, but Fabio dropped the Excel spreadsheet that I shared. You'll need to enable macros for it to work. But all I've done is take a simple Excel spreadsheet and copied and pasted in some Black Scholes option pricing code that I found online. If you've never done this before, you can't get the spreadsheet to work. You know, I can. I can tell you that all you really need to do is just kind of Google like, you know, Excel, vba, Black Scholes price, or. And you'll be able to find that somewhere. You know, there's a lot of examples out there. I've cleaned mine up a little bit more and verified it, so you probably would prefer to use mine. But you can pretty much copy paste this code off of plenty of sources on the Internet. All you need to do is get your developer tab open and go to Visual Basic and then you can copy and paste in the necessary code again.

[00:04:32.23] - Speaker 2
I've taken some extra time to register the functions and give them names and descriptions and stuff, but you don't even need all this. I've just added in a bunch of extra stuff so you can get delta theta, gamma, vega, but you really don't need much other than basically a simple pricer that can price calls and puts. That's what we've got here. I've created a simple function. And please again, throw in the comments if anybody's got questions or I'm going too fast. I'll try to pause and give breaks, but ideally everyone will be able to follow along in the spreadsheet. I've created a simple option pricer here. We're just using the simple Excel function BS Price, Black Scholes price. And it uses all these inputs that you can see highlighted.

[00:05:20.21] - Speaker 1
Ryan, maybe do you want to make it a little bit bigger? Maybe just.

[00:05:23.27] - Speaker 2
I'll make it even bigger. Absolutely. How's that?

[00:05:36.04] - Speaker 1
Perfect.

[00:05:38.07] - Speaker 2
All right, so, okay, so basically this is our function, our black Scholes price function. And you can see that it uses. And we can actually click this little FX button and we can see what the, what the inputs are. Sorry, I can't make that any bigger. But to price an option, you need the option type the underlying price P, the strike K, the time until expiry. This is typically measured as a number which is years. So in this case 0.208 is the. It's 0.208 years to expiry and then volatility, which is also an annualized percentage number. So 0.22, 22% implied volatility. I've also got optional arguments here for interest rate and dividend rate. I'm going to leave those out for today. But those can be accounted for in black Scholes. So that's pretty straightforward. You just need to put in those, those simple things and voila, you have your option price. I added an extra column for bumping the volatility if we want to see how it behaves. So this is a very simple one we've just priced here. You know, you'll see if I'm missing one of these, this is going to show an error.

[00:06:56.26] - Speaker 2
So if we're looking at, we'll use a nice simple example. So if SPX is trading at 550, interest rate is we always use for futures and options. On futures index options we always use interest rate and dividend of zero. That's also the case if you're pricing, you know, options on crude oil futures or gold futures or anything like that. The interest rate is 0. I won't go into detail why that is. Today we enter the expiration date from that I'm just calculating versus today when we're pricing over 365, you know how much time there is till expiry. Then what is the option? The strike price. So in this case we're talking about on SPX we're looking at the November expiry 580 call and I'm using 22 implied volatility. You know, it could vary and I didn't check the latest volatility, but this should be pretty close, give some reasonable results. And when you enter all that, you get a price of 10 spot 58. So there you go. And a delta of 31 which we'll go into more so the first thing that I'm just going to cover is, you know, is what drives the option price.

[00:08:15.03] - Speaker 2
Hopefully everybody knows that, but if you don't, that's fine too. I'm going to give you a very simple rule for remembering what the key drivers of option price are and what the key impact of those drivers is. When you're thinking about an option price, just ask yourself, if I had an option, what would I like? What would be good for me? You'd like more time to expiry because the longer you have, the more chance your option gets in the money. You like more volatility because the more the underlying is moving, the more that you know, the more chance that it'll get way in the money. And you would like your option to be closer to the money. You know, if you'd like the underlying price to go up relative to your strike. If you have a call and you'd like it to go down relative to your strike if you have a put. So it's not rocket science. If your options more in the money, the underlying is more volatile or you have more time, your option's worth more. And now we can just see that and demonstrate that with our, with our pricer. So what happens as the.

[00:09:19.28] - Speaker 2
So this is a call option. So we benefit as the market goes up. So let's watch the price as we increase the underlying. See, that's going to go from 550 to 560.

[00:09:29.16] - Speaker 1
Boom.

[00:09:29.26] - Speaker 2
Our price jumps up from 1058 to 1406. What happens as we increase as we reduce the time? If I make this October instead of November, it goes down from 14 to nine. And the same, if we bump the volatility up by 2%, our option price goes up from 14 to 16. So in every case, hopefully that's obvious. But just to make that even more obvious, I'm going to show you guys a nice visualization. So we've got this visual visualization tab as well on here. So I'm just going to quickly show. Let's see here. So let's look at. First let's look at implied volatility and look at the option price. So on the Y axis, we're looking at the option price should be. That doesn't look right. Right. And then, and then we're going to look at. So we're going to look at the option value. Hold on, it's using the wrong Y axis. So when we look at the option value here. Oh, yeah, that's right. No, it does. It goes up to 100. So that's correct. It's a big jump. All right, so first let's look at option value versus implied volatility. So if we make sure that the Underlying price is 450 in every case, And then we look at implied volatility and say that it increases by 1%, I'm going to zoom out a little bit so people can see.

[00:11:44.07] - Speaker 2
Oops. Okay, so now everyone can see what happens to our option price based on implied volatility. Again, we're pricing the 580 call here versus this. In this case, I have the underlying at 450. So you can see that as when volatility is, you know, 16%, that option is basically worthless. As implied volatility goes higher and higher and higher here, that option starts to rise higher and higher and higher and starts to approach about nearly $2. Now we'll keep implied volatility constant. So in this case, let's set implied volatility to be 16% the whole way. And now we're going to look at how the underlying price changes. So I'm going to have the price go up by 1.5% in each step. So now we're looking and seeing how as the underlying price changes again, the. The option value changes significantly. Just need to set this equal to. So that shows you how as the underlying price of SPX goes up, your option value changes. If anybody's seen the hockey stick before, for anybody who's familiar with the hockey stick, the hockey stick is the value of the option at expiry. And you'll notice that the gray line is the actual value when you still have time until expiry.

[00:13:34.05] - Speaker 2
So the hockey stick, for anyone who's not familiar, is basically saying, okay, if you take that option and expired it today, how much, you know, how much would you receive? If it's out of the money call option, you get zero. And if it's in the money, you'll get the difference between the current price and the strike price of your call option. But this gray line shows you that basically, you know, that this approaches the hockey stick. I'll show you a cool little trick here for those people who are familiar with the hockey stick trick. If we, if we increase the amount of time until expiry, so if we say Increase this to 25, See how much further it gets away. And so what's going on there is that you have more time value. So, so even these way out of the money options or way in the money options gain extra value because there's a lot more that can Go. That can happen in the coming months. Right. This should have been the same and quite do that. Right. But here we go. Okay, so you can see here that the less time you have, the more that it approaches this, this X free, this at expirator, it approaches the hockey stick.

[00:14:55.03] - Speaker 2
So hockey stick. The hockey stick is the right way to think of an option at expiry. But what Black Scholes formula on a pricer can show us is it can show us how we approach that hockey stick. So we're seeing underlying price. And then I'm not going to waste time doing the time, but if you want to do the same study, you can change your X value to equal expiration and then you can look and you can say set all these equal, like to equal to 450. And then you can set each time to be a little bit later than the last one. So you can start with 10, 18, 20, 24. And you can move it down, you know, bump it by was this plus, you know, seven days, for example, and you can look at what happens. I guess I just did it. That was pretty fast. So you can see what the option value does again. Okay, so there we've covered kind of the basic drivers of an option price and hopefully I've proved to you what the three key inputs are. So now that we've, you know, talked about what an option price is, let's think about risk.

[00:15:59.01] - Speaker 2
So let's see. Give me one second. Just checking my notes. Okay, so delta. So let's talk about delta now, because I think delta is probably the most common Greek, the most common kind of risk variable with perspective to options that you'll hear about. It's the first one that always comes up. And there's a lot of misunderstanding about delta. So delta, the common sense definition that most people use is delta is the percentage probability because delta always goes from 0 to 1 or 0 to 100. It can be negative if it's a put, you know, but. Well, different people measure that differently. But. So the most common thing that I've heard about delta is, hey, this is the probability it's going to end up in the money. That's okay for thinking about it, but it's not, it's not quite accurate. So today I'm going to actually show you what delta is. So in this case, you don't even have to worry about calculating delta because we have a formula called BS Delta. It uses all the same things as the pricer used. So that's pretty straightforward. Right, but how can we figure that out? If we don't have a formula, and how do we understand what that means?

[00:17:16.07] - Speaker 2
What does 0.38 mean about this? Right, so I'm going to give you a little example here. So whenever we talk about risk, forget about, just like I told you with thinking about the options price, you just want to, when you're trying to remember the key variables, you just ask yourself what's good for the option holder? What do they benefit from? More time, more volatility, you know, higher price if it's a call option. So, you know, whenever we think about risk, again, all risk boils down to is asking yourself the question, what's bad for me or good for me? What happens to my portfolio? What happens to my wallet, my P and L, my money if things change? And so that's really all we're gonna do with our option pricer. And this is exactly what the pros do, too. I'll show you how we can make it more complicated in a moment. But basically, if we want to see how the price of our option changes, because ultimately, if we bought this call option, this 580 call option, we want, we want the value of that call to go up. So we're going to see how it changes as the price goes up.

[00:18:21.08] - Speaker 2
It turns up. Delta is just a fancy way of saying, I want to know how much the value of my option is going to go up if the underlying price goes up. So we're just focusing on one of those three key variables that we talked about, time, volatility, and underlying price. So delta tells us how much this is going to go up. So let's note down here that when the underlying price is at 560, the price of the option is 1406. Now let's see what happened. Remember that this delta is 0.38. So let's see what happens when the price goes up to, say, 570. So when we put it up to 570, the price went up to 1821. I'm just gonna add, Okay, so when we move the price up to 570, the price went up to 1820. So what you can see is that the price going up causes an increase in the value of the option. So this isn't Vega, this is delta. So we're going to look and we're going to see that this is a, you know, this tells us that delta is going to be about 41 and a half.

[00:20:04.09] - Speaker 2
Anybody thinking back to their, you know, eighth grade math classes, remembering the slope of a line, we're just taking y2 minus y1 over x2 minus x1. But remember, this is, you know, just common sense. We're just saying how much does it change in X? In this case, 10 bucks increase the value of our option price. So what we found out is that for every dollar that, that, that the underlying increases, we're going to gain about 41 cents in our option price, which you can see because this went up $10 and we gained $4.15 roughly. We went from 1406-18. We gained $4.15. Now Delta, remember we solved 38 before. Delta is just for really small shifts. So remember this formula told us it was 38.132. So what happens if we just bump this a teeny tiny amount, so 560.1. So now if we take, if we just bump this 560.1, our option doesn't change much, right? 1409. Yeah. Oops, that looks off. I'll have to double check. Why? That's giving me a slightly goofy answer. I must have made a. Calculation mistake. But basically we saw before that the last one was, you know, it changed between 0.38 and 0.45. But basically that's all it's, all it's telling us is.

[00:21:59.29] - Speaker 2
So when we talk about a 50%, you know, at the money option, so when the market is at 580 and the strike is 580, we basically have a 52% delta. Right? And that's basically telling us that if the market price goes up by a dollar, we're going to make about 50 cents on our option. And you'll see that right here. Right. So when we bump the underlying price from 580 to 581, we'll go from 2307 to 23.59. So we made just a hair over 50 cents. And that's exactly what we expect, notwithstanding the fact that I typed in something wrong down here. But so again you're going to see 52% Delta. So when we bump our price 582 again, we're going to go up about 50 cents and that's going to continue. Now our delta changes, you'll notice it gets higher as the market goes up once we get really in the money. So once we get to say 625, let's go even higher. 650. Suddenly we have an 88 Delta. What does that mean? It means our option is way in the money and going back to our hockey stick. Let's, you know, when our time was constant and the Underlying price is what changed.

[00:23:29.25] - Speaker 2
So going back to this example, remember how the more time we had, the closer it got to this hockey stick? Yeah. Well, we're way out here, so we're basically getting close to the hockey stick. What that means is we're starting to move one for one with the underlying price. So what I mean by that is, now what happens if we go up by a dollar, Our options currently worth 7386. So if we go up to 651, we went up to 74. 74, so not quite a dollar. We increased by about 88 cents. So this Delta number is really just telling me for, hey, for a dollar move in the underlying or for a percentage move in the underlying, how much am I going to, you know, how much am I going to increase? Okay, so I guess. Any questions, Fabio, Will we see in the comments, Will I see questions? I haven't seen any questions yet.

[00:24:27.22] - Speaker 1
Yeah, we will see it. Let's see if we have any. Not yet.

[00:24:32.04] - Speaker 2
Okay, cool. So I'll just keep soldiering on. So hopefully that that's clear to everybody that the delta is just a simple. It's a simple calculation where we literally just look and say, all right, how much is this going to go up? If this, you know, if. If the underlying price increases, how much does our option price increase? And we can do the exact same thing. It turns out. It turns out when you make a really small change to this number, you're actually calculating the first derivative, which is the true definition of these. But again, you don't. You don't need to know that. It's just kind of fun to realize that when you're playing with this, you're actually doing some higher math. But again, with computers, we have the, you know, in the old days, you had to do this with paper and pencil, you know, and do advanced math. But we have the benefit with computers that we can literally just shock the price by a small amount or the volatility by a small amount and see how it changes price. And that actually tells us. And in fact, practitioners, you know, market makers prefer that to trying to do the underlying math.

[00:25:34.25] - Speaker 2
And the reason is because the underlying math gets really complicated, and if you have lots of different options or if you have more complex options. And so what we tend to do is it's better to just revalue our. All of our positions together with a new set of assumptions and see how the whole portfolio changes. So now I'm going to walk you through a quick example of that as well. So Real quick. Actually, before we walk through an example of a portfolio, I want to show you guys one other thing which is a lot of, I think there's a lot of question around how market makers actually trade and how they make money. So I'm going to give a quick example of how a market maker will make money and how they will trade. So let's look at delta and keep an eye on that and let's assume that our goal now rather than just speculating. Quick question here. I want to answer. Are you constantly updating the variables throughout the day manually? Usually we have an option pricer that pulls it in live. Usually we'll have an API feed into our pricer so that we can just, you know, pull in the live price.

[00:26:43.04] - Speaker 2
Implied volatility doesn't change that much. So usually an option trader will just use a manual bump. At least when I was trading, there's two ways you could do it. You could just, you could, you could pull in live implied volatility from the exchange or you can say, okay, you know, I think it's up. So yeah, the underlying price will actually be an API feed and then the volatility bump. We usually use end of day balls from the previous day and then, you know, and then tweak it as we're trading throughout the day. If our view is that volatility is changing, you know, and the other vault and the other inputs are pretty constant, like interest rates, we would usually just use the previous days. You don't have to worry about that. You know, if it was like a day of the Fed was changing rates and expiration is a known thing. So the good question, the answer is, yeah, you really only need to update the underlying price constantly. And then again you would move implied volatility. So just to follow up, why do I say it doesn't change that much? It does change, it just doesn't change that frequently and it doesn't change that large in magnitude compared to say the underlying price.

[00:27:55.29] - Speaker 2
So typically, you know, we don't see that big of a bump in volume. Usually a couple percentage points would be a really big jump in volatility. And often it's more like say half a percent. But usually as a market maker, we come in under the assumption that nothing's changed. And so if someone wants to buy, remember implied volatility equates to price for a market maker. So if implied. So if someone wants to buy my option and they're willing to pay me the offer, meaning higher than the mid value, that suggests there's Higher implied volatility? Well, I don't know. As a market maker, I can't be sure. Is that because implied volatility is up or is that just because somebody wanted to buy? Now if everybody keeps buying from me, then I need to assume that I'm selling it too cheap and at some point I bump up my implied volatility. So implied volatility does change, but it's actually the daily trade of the options that causes it to change. So what's happening is all the market makers out there are slowly changing their model. If everybody's buying options from them today, they need to bump their implied volatilities that they're using higher and that's what drives it.

[00:29:02.01] - Speaker 2
So again, the answer is, yeah, implied volatility definitely changes throughout the day. But you know, there's always a question for a market maker. Is the reason someone's buying because I'm earning the bid ask spread or is it because, you know, the market's moving and do I need to adjust my model? So that's, that's kind of what a market maker's main job is in the options market is to figure out what the correct implied volatility is to be using. So that's really their full time job, whereas the underlying price they just take as a given for the most part. Hopefully that answered the question. So, okay, so moving on, let's talk about, let's see where we're going to. Oh, we were going to talk about what Delta is for a market maker and how they would be hedged. So going back to our simple example, when the market's at 580 and you trade a 580 call, let's say as the market maker, you don't want to bet on the market going up or going down. You just want to earn the bid ask spread. You sold somebody or you bought this call option from somebody and your goal is to just not lose money.

[00:30:08.07] - Speaker 2
Right? So what can you do? How can you protect yourself? Assume you can't just turn around and sell the same option or you would give away all the bid ask spread that you earned. So what you do with your 580 call is you want to sell the underlying, you want to hedge yourself with the underlying because of what benefits a call. A call will benefit if the underlying goes up. And I just showed you exactly how much it will benefit. It will benefit by 0.52 cents for every dollar that the underlying goes up. So as a market maker, what do we need to do? We need to sell 52% of our option shares in the underlying market. So if this is an option on 100 shares, I need to turn around and sell 52 shares. If I do that and the market goes up just a little bit, if it goes up from 580 to 581, I'm gonna lose roughly 50 cents. There we went from 23.52 to 23.59. Right. Just showing you again. We went from or 23. Oh, sorry, 2307 to 23.59. But if I sold 52 shares, give or take, I'm gonna lose a dollar on those 52 shares divided by a hundred because I'm assuming my options on 100.

[00:31:28.08] - Speaker 2
So I'm going to do everything in percentages because that just makes it a little less confusing. But, so if you sold that those futures or those underlying futures or the index, in this case, since we're looking at spx, then you're fine. You don't care. You didn't make or lose money, right, because your option made 50 cents and your hedges, your short index futures lost 52 cents in total. And so that's, that's perfect. Right, but what's, but let's note what happens when the market goes up quite a bit. When it goes up to 600, suddenly my Delta increased. So what needs to happen? Let's just say the market suddenly jumps from 580 to 600. But remember, I'm a market maker. I'm not trying to bet on the market going up. Suddenly I'm effectively long because now I've sold about. I've sold 50% of my shares in the underlying market or my. Or my futures and the underlying market. But this delta tells me that if we go up another dollar, I'm going to make 65 cents. Here, I'll prove it to you. We should go to 35, 45, right. Four to six. Yeah. So being only short 50% is not hedged.

[00:32:47.18] - Speaker 2
Now I'm betting on the market going up and vice and vice versa. If it goes down, I'll lo. So. So I'll get to that question in just a second. Marco. So, okay, so what do we need to do as a hedger? We need to sell more. We were short 50%, right. So we. And. But now we need to be short 65. So we sell another 15 of our position of on the underlying. So again, if it was on 100 shares, we sell another 15 shares and that will make us indifferent. But notice what the price is. Now remember, we first did this trade at 580. And now it's at 600. And so we first sold, you know, about 52 shares at or 52 futures at. At 580. And now we're selling another 13 futures at 600. What happens if the market goes back down to 580? Ah, our Delta falls again. We're back to only needing about 52 futures to be, to be hedged. So we get to buy back those futures. We sold those. The extra 13 futures that we sold at 600, we get to buy them back at 580. Free money, right?

[00:34:08.20] - Speaker 2
So we just made money. And what happens if the market falls from 580 to 560? Our delta is only 38, so we don't need to have to be short all 52 futures. We can actually turn around and buy back 14 futures. And then what? And we're buying them at 560, lower than 580. And then if we go back to 580 again, ah, look, we get to sell those 15, 14 lots that we bought down at 560. We get to sell them again at 580. So you can see that hedging this option that we're long, we make money every time it moves. This is great. We can't go wrong. When the market rallies, we get a sell. When it falls, we get to buy back. It forces us to buy low and sell high. So we're actually making money. So the big question, so, so what could go wrong? I should just do this all day, right? Well, premium. So you have to pay an option premium. And for options traders, we call that theta. So every day. So. So that's really the answer to your question right there, Marco, is there's two ways that you can, you know, make money in options trading.

[00:35:27.00] - Speaker 2
Obviously, if you just sell a call option. If you just buy this call option and, you know, someone hits your bid and then someone just turns around. Sorry. If you buy it because someone sells it to you, and then someone turns around and immediately buys the same one from you for a little bit higher than where you bought the first one. Sure, you make money, but what happens if you don't have the chance to do that? Because usually you don't get that lucky. Someone's buying and selling at the same time. So you hope that you bought it at cheap enough implied volatility that you'll make money on this delta hedging game. Because remember, every time the market goes up and down, you get a hedge. And that's actually called Gamma. That is Gamma. So for everybody who's using Gamma and the Jacks calculations and all those things. Gamma is the act of delta changing. The formal definition is the second derivative. It's the second derivative of price with respect to the underlying. But really all you need to remember is oh my delta changes. And that's good for me if I have the option and that sucks if I'm short the option.

[00:36:32.12] - Speaker 2
Because it should be obvious from what we just showed that the exact opposite math works for you if you're short this option, right? So if you were short this option and the market went from 580 to.

[00:36:41.10] - Speaker 1
600.

[00:36:44.22] - Speaker 2
So let's do this again. So if the market's at 580 and you're short the option, then to protect against it going up because you're short a call, you need to, let's see here. So you're short the call option. So to protect against the market going. What you just said. Sorry. So LJ Quick gonna hit your question. That is gamma scalping. That is the difference. That is the definition of gamma scalping for a market maker. There might be some people who are, who are day trading based around the jacks numbers, based around the kind of open interest numbers and the key reaction levels that, that are published by Mentor Q. But, but the technical definition of gamma scalping for a market maker is what I just showed you. So when the market pops up, you know, then they're gonna, when the market pops up, they sell futures and when it falls back down, they buy futures. And they're doing that constantly. You're scalping your gamma and every time it moves up and down and up and down and up and down, you make a little bit of money. So the question is, but the problem is you have to pay premium for that option.

[00:37:55.26] - Speaker 2
So market makers have A or volatility traders because you don't just have to be a market maker to do this. You can just bet on implied volatility without having a view on the underlying market. If you just, if you think vault. So based on the implied volatility that you paid for the option, we can actually calculate a break even. And you'll have to bear with me here, I forgot to do this calculation in advance, but I'm 95% sure that the official formula we'll check if this is correct is going to be equal to implied volatility divided by the square root of in this case 250 trading days or 252 trading days times the underlying price. So for an at the money option with 22% implied volume, let's see if that looks right. I'm just going to double check my math here. Yep. So for an option, if we buy an option with implied volatility of. Yeah, we'll need the option to move 1.386% every day if it's got 22% implied volatility on average for us to make money gamma scalping. Because remember, the option premium is determined by the implied volatility. So all these other things are outside of our control.

[00:39:55.21] - Speaker 2
So if we buy this option with 22 implied volatility, I. E. We pay 23 cents for it, or sorry, 23 bucks for it, then we need this underlying to move 1.3% every day. Just turn that into a percentage. We need to move 1.3, 1.4% every day for us to make more money gamma scalping than we made in our delta hedging than we paid out in premium. And remember, each day we lose some of the premium we lose. We call this theta. But now that you guys understand how to calculate Greeks, you won't be intimidated by theta because it's very easy to figure out what our theta is. Our theta is simply saying, how much do I lose in option value if I get one fewer day to price this option? So what happens if we go from 1118 to 1117, so suddenly I lose an option. We were at 2307, now we're at 2291. So we lost about 18 cents. So we lost 18 cents for one day. So we need to effectively make 18 cents trading Delta to cover our theta, which was one day, a one day change. And again, like if you.

[00:41:19.18] - Speaker 2
For the nice thing though is you don't have to memorize these. A lot of people think, oh my gosh, I've got to go out there and memorize like, what, what is my Delta? What is my Gamma? What is my theta? What is Vega Vanna charm? Oh my gosh. And you start to, you feel like your head's gonna explode. But you don't have to do that because all you need to do is go just have an option pricer and then just change the inputs and see how much it changes your option price. Right. It's not rocket science. And this is all that, that options traders actually do. They just change the inputs and see how their P and L changes. So it's really quite simple. And all those fancy terms are for, is for just. They're, they're just definitions of the changes that we're doing. Anyways, theta equals. And I'll just write these down real quick so Everybody can see them. Theta equals our P L. How much we make or lose, gain or loss.

[00:42:16.20] - Speaker 1
What are you writing that? Okay.

[00:42:18.27] - Speaker 2
Yeah. Versus change in time. You know, Let me put that like that so you can see it. Delta is our P L. If we change in underlying price. Vega is our P L for a change in implied volatility. Remember, we saw how easy it was to estimate all those. All we had to do was change the underlying price. Boom, we saw. That's our delta. How much did the price change, Vega? We just need to bump our volatility from 22% to 23%. Oh, boom, we saw. Oops, sorry. That was a bump. Bump it from 22% to 23%, goes up to 24 from 23. So we make about a buck for a 1%. There's a little over a buck, right? Yeah, a buckle four for a 1% move. And theta. We just needed to change by a day our option pricer. So now you have. If you have an option pricer, without memorizing anything, I told you, you can just go out, figure out for a current trading option, you know, these key inputs, and then you can just. And figure out and set it. You'll need to adjust the implied volatility to get the same price.

[00:43:51.17] - Speaker 2
And then you can just tweak them and you can figure out exactly what risk you're running. So if you're saying, okay, I'm going to go buy Nvidia calls with, you know, whatever volume is, I don't know, something crazy, 70% ball or 45% volume, you can say, well, what happens if I buy my call and volatility falls from 45% to 25% because, you know, you know, this. It stops being such a meme stock or, you know, thing. Things calm down. What's my risk? Well, you. All you need to do is you need to just. You start with 45 volume, and then you change it down to 20, 22% and you see exactly the change in price. And that's technically your vega. That's for a very big change in the example I just gave you. And we usually calculate vega for very small changes. But if that's what you care about, that's what you should use because you don't actually care about Vega for an infinitesimal change. We're not Isaac Newton here trying to do calculus. We're trying to figure out, hey, what's this going to cost me in dollars if the market changes a lot? When I was running my risk book at Deutsche Bank, I would actually Instead of looking at my Greeks like, oh, what's the vega for my portfolio?

[00:44:59.19] - Speaker 2
I would say, what's my portfolio look like? I was trading AG futures at the time and I'd say, what's my portfolio look like? If corn goes to 450 and implied volatility, you know, or you know, 550 in a big rally because there's a drought and implied volatility spikes from 23 to 38. And we would walk through scenarios and then we cared about the scenarios actually way more than we cared about the particular Greek numbers because the Greeks change. The Greeks are smooth. Going back to this example, like, we can look at delta. I'm going to give you a visual representation of gamma. Now. So if we set Y equal to delta. So it might take me a minute here. Oh yeah, we've got delta right here. So if we just set. Did I do that right? Oh yeah, I have to turn off. See that? That's our delta. And this is actually a visual representation of gamma. So remember when we had an. At the money, when we had it at the money option, it was roughly 50 volatility. And you can see that right here. That's when the price is at 580 on the 580 call, it's about 50%, just like we showed you.

[00:46:29.28] - Speaker 2
And then it goes up, up, up, up, up. Right? As it gets more and more in the money. More and more in the money. More and more in the money, it approaches one, but it can't, once it gets to one, it can't really go beyond one. Right, because we remember we approached that hockey stick. So you know, our, the, the lowest delta we can have is zero. And the highest delta we can have is one. And this is gamma, which charted gamma. So you're now actually seeing the second derivative. But again, I tell people that because I think it's cool to know, hey, I'm actually doing really advanced math here. But you don't have to worry about that. Gamma is actually the slope of this line at each point. But again, don't worry about that. Okay, let's see a quick question from Mag. How would you build those scenarios? That depends on your risk system. So if I was doing this, we're going to actually walk through how I would build the scenario for your portfolio right now. But you know, if you're a professional trader, you have a more complex risk system and usually your risk system will let you build out some scenarios and, and then it would literally revalue our entire option book back in the day.

[00:47:35.02] - Speaker 2
Technology's gotten a lot better, so I doubt this would be this slow nowadays. But when I was doing it 15 years ago, I mean it would literally run our option valuation engine, which was much more complicated than Black Scholes and it would recalculate the entire massive book in 10 different scenarios. And we would define the scenarios and then we look at them and we'd have to make some manual adjustments to those scenarios. That was how we used to do it. But you can actually define your own if we're just worrying about. But I'll walk you through a simple example of how we can define a scenario. Let's try that. It's a great exercise for us to do together. So now in practice we're not usually just going to trade one single option, right? We're often going to trade multiple options. So let's imagine now that we want to say buy the at the money call. But we're cheap, we don't want to pay too much option premium. So we're going to sell like the 620 call. Just going to copy those things down. Oops, sorry. Underlying price is always going to be equal to 580.

[00:49:00.29] - Speaker 2
So now we're doing a little a three way trade. Maybe we'll foreign. Let's say that we buy a call, then we're going to sell this call and maybe this is 20 implied volatility. It's worth remembering that implied volatility is not the same at every single point on the curve. And then let's see here. So, and then we next we want to do so we're going to buy the 580, sell the 620 and to help pay for our call spread, since we're bullish, we're going to sell a 520 put. Let's say that that has 24%. All right, so let's say that we bought here. I'm going to zoom out a little bit so people can see here. So we bought 10 of these, we sold 10 of these, and we sold 10 of these. So when we talk about scenario analysis, this is our scenario. So the scenario that we're living in right now is today it's the current state of the world. The market's at 580, no time has passed. And these are the implied volatilities. Now let's say we want to bump those, right? So here what I've done is I've calculated our portfolio value, the present value of our portfolio.

[00:50:44.29] - Speaker 2
So I've taken each of these prices of the options Multiplied it by our position and then. And then multiplied it by 1000, which is just the contract multiplier for SPX index options. So it's just that you multiply by a thousand bucks. So if you buy this call at 23 bucks and it goes up to 24, then you make $1,000. So that's all I've done here. So we have $108,000 of option premium that we're net long in this scenario. So let's go ahead and see what happens. Let's go ahead and see. You know, I'm going along with this for you guys. It's important. I didn't want to pre plan too much of this because I wanted to make sure that we work through the math together. So let's see what happens if we bump volatility by by 1%. That's Vega. Remember right here you can see it. What's our P L if implied volatility changes. So implied volatility goes up 1%. So we're actually. So we're losing money in this scenario. So when implied volatility went up, we lost about 4,000 bucks. Right. So when volatility goes up by one. Let's see if I get my video right here.

[00:52:13.26] - Speaker 2
So 1% from 0%. And Y1 was 100. And originally our P&L was worth 108,224. And now it's. And once we increase volatility 1%, now we only have 104,213. So it should be that we lost $4,000. There we go. We lost $4,000 over a point. Oh, one. Oh. For a 1% change in Vega. So that's actually. That's it. For a 1% change in volatility, we lose $4,000. It's that simple. There's no more complicated math than that. That's because I only bumped it 1%. If we bumped it 2% or 5%, we would change this to 5% and we would change this to the new one, which is 84. 256. Now we would need to divide this by this minus this. 0.05. Let me see. What am I doing wrong here? It was 20,000 over a 5% bump. All right, there we go. We want to know for a 1% bump. So we know what changes for a 5% bump. So we need to multiply it by 0.01 to get a 1% bump. So, so we know that for a 1% bump, it's going to change by about 4800 bucks. And again, we did this for our whole portfolio.

[00:54:44.29] - Speaker 2
So we can, we can calculate each of these changes individually. It's actually called doing the partial derivative. So we can figure out for our scenario what the whole book would be if we change the. So again, we knew here that. So now instead of worrying about the Greeks, let's just say scenario one and scenario two. And we can just define it, right. We know what scenario one is underlying 580 time is, you know, time to X free is. What's that? Let's just say 0.205, 0.205 times 365. And our. So it's 74 days. I do that, right? Yeah, about 74 days till expiry. And implied volume is basically 22%, 20% and 24%. And then, and we know what that leads us to. It gives us 104,000 of option premium. Premium. Actually in this case it gives us 80. Oh yeah, without the bump. 108, 000 of option premium that we're long. It's the present value of our book. So if we want to try a whole new scenario. So let's say, okay, let's see. I'm worried about. I put on this position and in, you know, let's say a month passes, so it's going to change to.

[00:56:43.09] - Speaker 2
We can just reduce it to 10, 17, 20, 20, 20 10, 18, 20, 24. And let's say that implied volatility goes up 2%. And the underlying price falls. So you say to yourself, hey, I'm worried that this, the S P is going to sell off, you know, and people are going to get nervous and implied volatility is going to go up. And so if that happens or that in a month from now, what will my new position be? 30 grand. So that's a pretty bad scenario for us. We would lose, we would lose about $78,000 in that situation. So that's not a good scenario for us. But that's important to know because you know, if you think there's a decent chance of that happen happening, this is a pretty terrible position for you because you're not just losing money from your, you know, from, you know, from the market falling. You're kind of losing it all on all ends. You're longing at the money options. You're paying theta and times going by and your short volatility, your next short vega. So when your implied volatility goes up, you get hurt and you're short of putting the market's falling towards that and away from your call that you're on.

[00:58:21.23] - Speaker 2
So not a good scenario. But, you know, it's important to know that as a trader, it's always important to know your downside. So I'm gonna stop here. We could theoretically calculate the Greeks for each of these trades and then sum those by position, and they should match exactly with this math we just did. But hopefully this was good for a start, for an initial lesson. When people talk about risk management, this is really all you're doing. You're just saying, hey, I tell me how much money I make or lose if something changes. And if you think about it again, you know, forget the math. That's what matters. How much do I make or lose if something changes? And all those Greeks, you can see them, you can Snapchat them right here. They're just a fancy way for. For options traders to discuss that.

[00:59:03.16] - Speaker 1
Awesome. Yeah, thank you. This was awesome. So we have a couple of minutes left. Let me know, guys, if you have more questions. All of these, all of our contacts, you can find them@mentor key.com and if you have any questions about this session, about the spreadsheet, we're going to share that inside the membership. So you're going to get access to the. To the. To the spreadsheet that Ryan presented. You can contact [email protected] or you can find it directly on Discord. So, yeah, please let us know if you have any questions. As always, And for those who are participating in the live session, we are providing you guys with the coupon code that you can use if you guys want to join us. So you can use this coupon to join our membership. And I think the next session with you, Ryan, would be something in this line. We're going to look at Greek scan. We don't have the schedule yet, but we'll set it up. So we'll keep you guys posted. And I think, you know, this is. Yeah, this was just great, showing how to manage risk, how to look at Greeks when looking at options.

[01:00:22.09] - Speaker 2
Yeah, terrific. Yeah, I look forward to, you know, getting more great questions and please reach out if anybody has anything. Thank you again for joining and, yeah, look forward to more teaching sessions.

[01:00:34.05] - Speaker 1
Thank you, guys. Have a good day.